parrice: Estimate the Parameters of the Rice Distribution

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Estimate the Parameters of the Rice Distribution

Description

This function estimates the parameters (\nu and \alpha) of the Rice distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments are complex and tabular lookup is made using a relation between \tau and a form of signal-to-noise ratio \mathrm{SNR} defined as \nu/\alpha and a relation between \tau and precomputed Laguerre polynomial (LaguerreHalf).

The \lambda_1 (mean) is most straightforward

\lambda_1 = \alpha \times \sqrt{\pi/2} \times L_{1/2}(-\nu^2/[2\alpha^2])\mbox{,}

for which the terms to the right of the multiplication symbol are uniquely a function of \tau and precomputed for tabular lookup and interpolation from ‘sysdata.rdb’ (.lmomcohash$RiceTable). Parameter estimation also relies directly on tabular lookup and interpolation to convert \tau to \mathrm{SNR}. The file ‘SysDataBuilder01.R’ provides additional technical details.

Usage

parrice(lmom, checklmom=TRUE, ...)

Arguments

lmom	An L-moment object created by lmoms or vec2lmom.
checklmom	Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \tau_4 and \tau_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check. However, the end point of the Rice distribution for high \nu/\alpha is not determined here, so it is recommended to leave checklmom turned on.
...	Other arguments to pass.

Value

An R list is returned.

type	The type of distribution: rice.
para	The parameters of the distribution.
source	The source of the parameters: “parrice”.
ifail	A numeric failure mode.
ifailtext	A helpful message on the failure.

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

See Also

lmomrice, cdfrice, pdfrice, quarice

Examples

## Not run: 
  parrice(lmomrice(vec2par(c(10,50),   type="rice"))) # Within Rician limits
  parrice(lmomrice(vec2par(c(100,0.1), type="rice"))) # Beyond Rician limits

plotlmrdia(lmrdia(), xlim=c(0,0.2), ylim=c(-0.1,0.22),
           autolegend=TRUE, xleg=0.05, yleg=0.05)
lines(.lmomcohash$RiceTable$TAU3, .lmomcohash$RiceTable$TAU4, lwd=5, col=8)
legend(0.1,0, "RICE DISTRIBUTION", lwd=5, col=8, bty="n")
text(0.14, -0.04,  "Normal distribution limit on left end point"   )
text(0.14, -0.055, "Rayleigh distribution limit on right end point")

# check parrice against a Maximum Likelihood method in VGAM
set.seed(1)
library(VGAM) # now example from riceff() of VGAM
vee <- exp(2); sigma <- exp(1); y <- rrice(n <- 1000, vee, sigma)
fit <- vglm(y ~ 1, riceff, trace=TRUE, crit="c")
Coef(fit)
# NOW THE MOMENT OF TRUTH, USING L-MOMENTS
parrice(lmoms(y))
# VGAM package 0.8-1 reports
#     vee    sigma
# 7.344560 2.805877
# lmomco 1.2.2 reports
#      nu    alpha
# 7.348784 2.797651
## End(Not run)

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.